In order to obtain all the inequivalent reductions, we look for the one-dimensional optimal
systems (see [1]}). These systems, similarity variables and reduced equations are listed below.
In the following tables REF , REF , REF , each row shows the infinitesimal generators \(Q_i\)  of each optimal
system, as well as its similarity variable, similarity solution and reduced equation. \(\alpha \)  is an
arbitrary constant, while \(\lambda \)  is a non-vanishing arbitrary constant. Note that in the case
\(f(u) = u^m\)  which corresponds to Eq. (REF ), we only consider \(m\ne 0\) , otherwise the equation is linear.
